Gravitational lensing by ring-like structures

We study a class of gravitational lensing systems consisting of an inclined ring/belt, with and without an added point mass at the centre. We show that a common feature of such systems are so-called pseudo-caustics, across which the magnification of a point source changes discontinuously and yet remains finite. Such a magnification change can be associated with either a change in image multiplicity or a sudden change in the size of a lensed image. The existence of pseudo-caustics and the complex interplay between them and the formal caustics (which correspond to points of infinite magnification) can lead to interesting consequences, such as truncated or open caustics and a non-conservation of total image parity. The origin of the pseudo-caustics is found to be the non-differentiability of the solutions to the lens equation across the ring/belt boundaries, with the pseudo-caustics corresponding to ring/belt boundaries mapped into the source plane. We provide a few illustrative examples to understand the pseudo-caustic features, and in a separate paper consider a specific astronomical application of our results to study microlensing by extrasolar asteroid belts.